Question

25.
The distance a spring will stretch varies directly with how much weight is attached to the spring. If a spring stretches 6 inches with 80 pounds attached, how far will it stretch with 55 pounds attached? Round to the nearest tenth of an inch.

Answer 1

To solve the problem, we'll use the fact that the distance a spring stretches varies directly with the weight attached to it. This can be expressed with the equation:

\[
d = k \cdot w
\]

where:
- \( d \) is the distance the spring stretches,
- \( w \) is the weight attached to the spring,
- \( k \) is the constant of variation.

From the problem, we know that when \( w = 80 \) pounds, the spring stretches \( d = 6 \) inches. We can use this information to find the constant \( k \):

\[
6 = k \cdot 80
\]
\[
k = \frac{6}{80} = \frac{3}{40}
\]

Now that we have the value of \( k \), we can find how far the spring will stretch when \( w = 55 \) pounds:

\[
d = k \cdot w
\]
\[
d = \frac{3}{40} \cdot 55
\]

Calculating this value:

\[
d = \frac{3 \cdot 55}{40} = \frac{165}{40} = 4.125
\]

Now rounding to the nearest tenth, we get:

\[
d \approx 4.1 \text{ inches}
\]

Thus, the spring will stretch approximately **4.1 inches** with 55 pounds attached.